The article deals with the problem of ensuring the long-term preservation of legally significant electronic documents. A review of the problem and existing options for its solution is made, the problem of ensuring the long-term preservation of legally significant electronic documents is formalized as an optimal control problem under parametric disturbances. Document safety indicators and mathematical models for evaluating safety indicators are proposed. The result of the study are algorithms that allow, being implemented in the form of software and hardware, to control and organize long-term preservation. Examples of the practical implementation of the proposed approaches within the framework of large information systems are given. The advantage of the proposed algorithms and approaches is that their implementation will make it possible to comprehensively solve the important scientific and technical problem of organizing the long-term preservation of legally significant electronic documents. At the end of the article, further prospects for research aimed at solving the problem of long-term preservation of big data and systems built using distributed ledger technologies are identified.